CHAPTER 11 Bar Cutoff

Transcription

1 page 188 CHAPTER Anchorage of Tension Bars by Hooks In the event that the desired tensile stress in a bar cannot be developed by bond alone, it is necessary to provide special anchorage at the ends of the bar, usually by means of a 90 o or a 180 o hook. The dimension and bent radii for such hooks have been standardized in the ACI Code as shown below. Standard Bar Hooks See ACI 7.1

2 page 189

3 page Development of Standard Hooks The Code requirements account for the combined contribution of bond along the straight bar leading to the hook, plus the hooked anchorage. A total development length l dh is defined as shown below and is measured from the critical section to the farthest point on the bar, parallel to the straight part of the bar. ACI Development length l dh in inches, for the deformed bars in tension terminating in a standard hook shall be computed as the product of the basic development length l hb and the applicable modification factor or factors given below, but l dh shall not be less than 8d b nor less than 6 in. ACI ACI ACI ACI ACI ACI ACI A s required A s provided Lightweight aggregate concrete 1.3 Epoxy coated reinforcement 1.2 ACI 7.2

4 page ACI According to ACI , for bars hooked at the discontinuous ends of members with side cover and top or bottom cover less than 2.5 inches, as shown below, hooks must be enclosed with closed stirrups or ties along the full development length. The spacing of the confinement steel must not exceed 3 times the diameter of the hooked bar. In such cases, the factor 0.8 of ACI does not apply.

5 page Example of Development of Hooked Bars in Tension Referring to the beam shown below, the No. 11 negative rebars are to be extended into the column and terminated in a standard 90 0 hook, keeping 2 in. clear to the outside face of the column. The column width in the direction of beam width is 16 in. Find the minimum length of embedment of the hook past the column face, and specify hook details. l hb = 1200d b fc = (1200)(1.41) = 27 in Side covers exceed 2.5 in. for No. 11 bars, and cover beyond the bent bar is adequate; therefore, the modification factor of 0.7 can be applied. l dh = (27) (0.7) = 18 in. < 19in. ok

6 page Code Provisions for Development of Web Reinforcement

7 page Development Bars in Compression Reinforcement may be required to develop its compressive strength by embedment under various circumstances; e.g., where bars transfer their share of column load to a supporting footing or where lap splices are made of compression bars in columns. In the case of bars in compression, a part of the total force in transferred by bond along the embedded length, an a part is transferred by end bearing of the bars on the concrete. Because the surrounding concrete is relatively free of cracks and because of the beneficial effect of end bearing, shorter basic development lengths are permissible for compressionbarsthanfortensionbars. If lateral confinement steel is present, such as spiral column reinforcement or special spiral steel around an individual bar, the required development length is further reduced. Hooks such are not effective in transferring compression from bars to concrete, and if present for other reasons, should be disregarded in determining required e3mbedment length.

8 page BarCutoffandBendPointsinBeams Usually, prismatic beams with constant concrete cross--section dimensions are usually used to simplify formwork and thus to reduce cost. It is common practice either to cut off bars where they no longer needed to resist stress, or sometimes in the case of continuous beam, to bend up the bottom steel to provide tensile reinforcement at the top of the beam over the support. Rational: Required steel area is calculated at maximum moment location; Less steel will be required at other points. let z=d--a/2, then M=Tz,orT = M/z The value of z (lever arm) will be smallest when at maximum moment section, but will not vary widely. Thus, we are being conservative if we proportion steel according to bending moment. (T proportional to M). For economy, we would like to keep expensive steel as highly stressed as possible. -- See the figure in the next page: For simply supported beam with uniform loading, 100% of the tensile steel required at center of the span where the moment is maximum and 0% is required at the support.

9 page 196 Continuous beam with moment envelope resulting from alternatte loading (e.g., see below)

10 page ACI Moment Coefficients (ACI 8.3.3)

11 page ACI Development of Positive and Negative Moment Reinforcement

12 page Standard Cutoff or Bend Points for Bars in Approximately Equal Spans with Uniformly Distributed Loading

13 page Shear Complication where a Bar is Cut off

14 page Special Requirement Near the Point of Zero Moment U = dt dx and dt = dm dx u = dm dx 1 Z = V Z a = M n V u If bars in question were fully stressed at a distance a to the right of the point of inflection (PI), and the moments diminish linearly to the point of inflection, as suggested by the dashed line, then pullout will not occur if the development length l d did not exceed the distance a. l d M n V u + l a l d 1.3 M n V u + l a Eq of ACI When ends of reinforcements are confined by compressive reaction as at the end of simply supported spans